Tickets for the 20-minute Oresundstag train service (00 46 7717 77711; oresundstag.se) to Malmo station (2) cost SEK107 (£11; departures every 10 to 20 minutes from 5.30am to midnight).

Buses operated by Swebus (00 46 771 218 218; swebus.se) and Nettbuss (00 46 771 151 515; nettbuss.se) cost from SEK49 (£5), but journeys are slower and much less frequent, each offering two to five Malmo-bound services a day. Taxis leave from Terminal 3, charging around SEK750 (£79).

Get your bearings

Skirting the coastline in a fertile stretch of southern Sweden that was once controlled by the Danes, Malmo is far closer to Copenhagen than it is to Stockholm. More than 350 years have passed since the Swedes forced their neighbours to leave, but the city retains a distinctly Danish feel, with broad, café-edged streets stretching out from a medieval centre with its own moat-ringed Renaissance castle (3).

South of the historic centre is Mollevang storget (4), the market square in the middle of Malmo's old working-class district, which today knots together some of Sweden's most culturally diverse streets.

Midway between the Old Town and the increasingly fashionable harbour area is Malmo station (2). The Skanetrafiken desk here (skanetrafiken.se; weekdays 6am-8pm, Saturday 9am-6pm, Sunday 10am-6pm) sells a 24-hour pass allowing unlimited travel on inner-city bus and train routes for SEK65 (£7). Cash is not accepted on public transport.

The tourist office (5) is at Skeppsbron 2 (00 46 4034 1200; malmotown.se; open weekdays 9am to 5pm, weekends 10am to 2.30pm), just west of the station.

Stroll west to pick up Engelbrektsgatan, and then head south until you arrive at Gustav Adolfs Torg (1), with the city's old neoclassical theatre, now home to a branch of H&M (12), on your left. On the southern side of the square is pedestrianised Sodra Tullgatan. Follow it south to the soupy green canal that wraps around the Old Town, then cross the bridge (13) and continue straight on to Regementsgatan, which marks the start of modern Malmo.

Window shopping

Independent clothing boutiques make the area around Davidshallstorg a big hit with fashion-conscious locals. Preppy menswear shop Ljunggren (14) at Davidshallstorg 1 does a good line in British breeches, plaid shirts and pocket watches (00 46 407 9900; mrljunggren.com).

Opened on nearby Karleksgatan at the start of this year, Love Street Vintage (15) is popular with young mums looking for heels, accessories and polka-dot dresses (00 46 7333 92171).

Lunch on the run

Lebanese immigrants brought falafel to Malmo in the late 1980s, and it soon became the city's favourite snack. The most popular place is the simple Falafel No 1 (16) at Bergsgatan 37 (00 46 7082 40266; falafelnr1.se), where a wrap stuffed with falafel and salad with hot sauce is SEK35 (£4).

Take a ride

From Mollevangstorget, around the corner from Falafel No 1 (16), board a bus to Malmo Konserthus or Malmo Centralstation (2), and transfer to bus 32 for the 20-minute ride to Ribersborgs Kallbadhus (17). This open-air bathhouse juts out into the Oresund Sound – the straight separating Denmark from Sweden (00 46 4026 0366; ribersborgskallbadhus.se). Locals have been braving the bracing, salty swims here since 1898, encouraged by claims about the icy water's mood-lifting properties. Adults SEK55 (£6).

More traditional is Arstiderna (20), in a red-brick building at Frans Suellsgatan 3 (00 46 4023 0910; arstiderna.se), which dishes up cured salmon with dill-creamed potatoes for SEK175 (£18).

Day Two

Sunday morning: go to church

Consecrated at the beginning of the 14th century, St Petri Kyrka (21) at Goran Olsgatan is Malmo's oldest church (svenskakyrkan.se/malmo; free; daily 10am to 6pm). Much of the vibrant art that daubed the cathedral's interiors was chiselled away in the 19th century and replaced with stark stretches of white paint, making the exterior's brick gothic spires the main focus for cameras. Mass starts at 11am on Sundays, and there are free organ recitals at 12.10pm Wednesdays.

Out to brunch

Gustav Adolf (22), with an outdoor seating area facing Gustav Adolfs Torg (00 46 40 611 2272; gustavadolf.com), puts on a good-value brunch buffet between 11am and 4pm every Sunday (sittings at 11am and 1pm). For SEK165 (£17) you can work your way through a seven-metre-long table of hot and cold food, including local dishes and exotic fruit.

A walk in the park

Criss-crossed by canals, duck ponds and meandering cycle paths, the three parks surrounding Malmo castle (3) are a tranquil haven for sunbathing Swedes.

Slottsparken (23), the biggest of the three, was a military training ground until the end of the 19th century. These days it's one of the more serene locations for taking in views of the Turning Torso (24), the twisting white skyscraper that – at 190 metres – is Scandinavia's tallest building.

Cultural afternoon

Danes built the blood-red towers that flank the castle (3), but it was the Swedes who surrounded them with a moat. Dug in the 17th century, the treacherous trench helped scupper Denmark's attempt at recapturing the castle.

The sprawling Renaissance-style complex beyond the moat now houses Malmo Museer (00 46 4034 4437; malmo.se/museer; 10am- 5pm daily), a well-kept collection of museums that includes medieval treasures, archaeological exhibits, an aquarium and science centre. A ticket for all the museums is SEK40 (£4) but under-20s go free.